Problem: The sum of two numbers is $76$, and their difference is $26$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 76}$ ${x-y = 26}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 102 $ $ x = \dfrac{102}{2} $ ${x = 51}$ Now that you know ${x = 51}$ , plug it back into $ {x+y = 76}$ to find $y$ ${(51)}{ + y = 76}$ ${y = 25}$ You can also plug ${x = 51}$ into $ {x-y = 26}$ and get the same answer for $y$ ${(51)}{ - y = 26}$ ${y = 25}$ Therefore, the larger number is $51$, and the smaller number is $25$.